In the following problem, "=" stands for "÷", "+" stands for "-", "×" stands for "=", "−" stands for "+" and "÷" stands for "×". Which of the following coded equations is actually arithmetically correct?

Introduction / Context:
Here you are given a code for mathematical signs and must determine which one of the given equations becomes a true statement after decoding. Each symbol in the options does not carry its usual meaning; instead, there is a mapping given in the question. This type of problem evaluates accuracy in symbol substitution and careful checking of several alternatives.

Given Data / Assumptions:

- "=" stands for "÷" (division).
- "+" stands for "-" (subtraction).
- "×" stands for "=" (equality).
- "−" stands for "+" (addition).
- "÷" stands for "×" (multiplication).
- We must test each option by translating all symbols according to this mapping and then checking if the resulting arithmetic equation is correct.

Concept / Approach:
For each option, replace every symbol with its true operation. Where "×" appears, it should become "=", meaning that the location of the equality sign may shift. After decoding, the left-hand side and right-hand side must be evaluated using standard arithmetic precedence. The correct option is the one where both sides are equal numerically.

Step-by-Step Solution:
Consider option C: 5 ÷ 3 − 25 + 20 = 20 × 39. Apply the code mapping symbol by symbol. "÷" stands for "×", so 5 ÷ 3 becomes 5 × 3. "−" stands for "+", so − 25 becomes + 25. "+" stands for "-", so + 20 becomes − 20. "=" stands for "÷", so = 20 becomes ÷ 20. "×" stands for "=", so 20 × 39 becomes 20 = 39. Thus the decoded equation is: 5 × 3 + 25 − 20 ÷ 20 = 39. Step 1: Evaluate the left-hand side with precedence. Compute 5 × 3 = 15. Compute 20 ÷ 20 = 1. So the expression becomes: 15 + 25 − 1. Now compute 15 + 25 = 40. Then 40 − 1 = 39. So the left-hand side equals 39, which matches the right-hand side.

Verification / Alternative check:
We can quickly test the other options similarly and see that none of them produce valid equalities once decoded. Option A, for instance, does not balance after the conversions and arithmetic. Option B likewise leads to left and right sides that differ. Option D is incomplete as an equation. Hence, option C is the only valid decoded equation.

Why Other Options Are Wrong:

- Option A yields a left-hand side that does not simplify to the right-hand value after decoding and evaluation.
- Option B produces a mismatch between left and right sides, even though at a glance it seems simple.
- Option D does not even form a proper equality once symbols are decoded.

In all these cases, the decoded equations are not true.

Common Pitfalls:
A typical error is to change only some symbols or to forget that "×" actually produces an equality sign, not a multiplication. Another common mistake is to ignore operator precedence when simplifying the left-hand side after decoding. Writing out each transformed expression clearly and then simplifying step by step avoids these traps.

Final Answer:
The only equation that becomes correct after decoding the signs is 5 ÷ 3 − 25 + 20 = 20 × 39 (option C).